Gibbs sampling is a special case of the Metropolis-Hastings algorithm. From a given state of the variables it randomly moves to another state, preserving the desired equilibrium distribution. The simplest version is single-site Gibbs sampling, where each variable is visited in turn and sampled from its conditional distribution given the current state of its neighbors. Variables may be visited in any order and some variables may be sampled more than others, as long as each variable gets sampled sufficiently often.
The Gibbs sampling algorithm object has two configurable properties:
- BurnIn: number of samples to discard at the beginning
- Thin: reduction factor when constructing sample and conditional lists in order to avoid correlated samples
Gibbs sampling typically requires many more iterations than EP or VMP (each iteration is one sample).
When choosing an inference algorithm, you may wish to consider the following properties of Gibbs sampling:
- Gibbs sampling will eventually converge to the correct solution, but may take a long while to get there.
- Speed of convergence may be helped by careful initialisation.
- Gibbs sampling only supports conjugate factors - i.e. marginal posteriors and conditional distributions over any variable in the factor have the same parameteric form as the prior for that variable.
- Non-conjugate factors require more sophisticated Monte Carlo methods which are not currently supported by Infer.NET.
- Gibbs sampling allows you to query for (a) posterior marginals, (b) a list of conditional distributions, and/or (c) a list of samples. See QueryType in Running inference.
- Gibbs sampling does not support variables defined within a gate, but does support mixture models which only have factors within a stochastic If, Case, or Switch statement.
- Gibbs sampling is stochastic - it will give different samples depending on the random seed for different initialisations. You can read about how to change message initialisation